I can only think of seven examples of magic in A Song of Ice and Fire (not counting supernatural creatures that don't have supernatural abilities, like Wights, Dragons, or Others).
Others have supernatural abilities - they clearly are able to freeze things, and craft swords and the like out of ice. They also are implied to be able to create the wights in the first place.
And dragons, well, maybe they don't cast spells, but they're tied into supernatural stuff, and apparently have powers over magic, if only as a source.
1) Bringing people back from the dead. This trumps mundane fighting 100% of the time, because you can't win a fight against something that keeps coming back. Possibly limited in some way, otherwise why not bring back your entire army?
But you're still just bringing back the same guy again. Access to resurrection magic is great, but effectively it's still just another sword. I get your point here, resurrections are pretty uber, but you're still limited by the material - the resurrected individual is still the same individual. Sort of. Not really. We don't really know what changes, but yeah...
2) Lighting the dragonglass candle in the Maester's ritual. This is supposed to be impossible, and is kind of useless anyway.
Yup. Useless.
3) Skin-Changing. Better than mundane fighting, unless you can kill a bear, a wolf, and a shadowcat back-to-back.
Generally true - but GoT Wargs are still a long way off from actual shape-changing. The animals in question get some intelligence bonuses, but they're still just animals.
4) Divinations. Powerful, but not 100% accurate. This includes both fire-gazing and greenseeing. Firegazing seems to be the easiest magic to learn.
Divination in the hands of a smart user will probably always be the most dominating form of magic. Preparation always equals wins. I'll give this one to you. Its worth noting though that the casters generally need sword-arms or stone walls handy to protect themselves against attackers.
5) Face-Changing. Better than being sneaky.
Its certainly nice when trying to get away. I'm not sure if it adds much power to someones sword arm though. I don't recall anyone being able to mimic an existing face, which is where face-changing assassination really gets effective.
6) Shadow-birthing. Appears to be 100% effective, but physically draining to the... "parents". Also limited by proximity to the target, and time (takes a few days' gestation)
Yeah, this is the big deal in the setting. I'm not even sure if distance is a real defense - they weren't getting close when Davos took them under Storm's End, they were getting past the walls with their ancient defensive magics.
7) Fire manipulation. Not sure if this can be used offensively, or just for entertainment.
We've had flaming swords, but their value seems largely psychological. I suppose the wildfire seems to be magical alchemy which can be used offensively.
I can think of only 2 examples where mundane strength beat magic:
1) Jon Snow killing Orell
2) Denarys killing the Undying Ones (this might not count, because the warlocks don't actually seem to do any magic)
So, even in a setting where magic is supposed to be super rare and costly, you're still better off being magical than mundane.
I wouldn't say Dany killed the undying ones - Drogon did it. Dragons > Magic. Or perhaps Dragons = Magic. It's not entirely clear what the relationship is, but it seems that a dragon will pretty much always trump various supernatural things.
Also:
3) Dany (and her army) took down the Maegi lady (twice, technically). All the Maegi really managed was to force a miscarriage.
4) Samwell, despite lacking anything resembling martial ability, took down an Other with a knife. You could argue that his win was based on a magic item, or exploiting a weakness, but still - it was an obsidian knife, thats all.
Keep in mind that the main reason its hard to find examples of mundanes trumping magic is because almost none of the magic has been confrontational. Of the six types of magic you listed, only one involved magic targeting an individual.
It also isn't clear how hard it is to learn magic. Some of it seems divine in nature - the fire magic in particular, but we have no idea how hard it would be to become a priest of the fire god. Wargs seem to be a bloodline thing - it can be learned, but you need ability to start with. Greenseeing is the same. It seems like anyone could learn to change their face - but we're not sure how much effort is involved. In DnD terms magic is probably on a par with taking a prestige class, or maybe even just a feat in some cases.
I'll agree with you, magic is certainly an advantage. However, other than a few assassinations, it doesn't seem to be much of a game changer. No one is teleporting through walls, single-handedly defeating armies (unless you're Aegon the Conquerer with a handful of dragons)(I'd probably argue that the dragons
are an army), altering the landscape, or otherwise throwing down 'I win' buttons. In other words, the magic there is largely used for utility (scouting functions, and a few social ones) rather than combat. In combat, the sword seems to still usually win.